Supervised Learning with Quantum Measurements

TL;DR

This paper introduces a quantum-inspired supervised learning method that uses quantum measurement formalism to classify data without parameter optimization, demonstrated on 2-D benchmark problems.

Contribution

It presents a novel quantum measurement-based classification approach that generalizes Bayesian inference and kernel methods, eliminating the need for parameter learning.

Findings

Effective on 2-D benchmark classification tasks

Does not require parameter optimization

Can be implemented with various quantum encodings

Abstract

This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the relationship between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the output. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.